Hi OP - I’m in a similar position, but two years further down the line.
Speaking from experience - the only situation in which you should stay another 3 months ‘to see’ if anything changes, is if you think there is a good chance your mind might change in that period. If you know, with certainty, that it won’t, then you should make your plans to leave now. It’s not fair on him to expect him to change his mind, he has at least (unlike my partner) been very honest with you about his views. Staying will just make the decision and outcome harder for you, and you alone.
My situation is a bit different. My partner and I both want kids, but I am ready (at the timeline we discussed early in our relationship), while he is not. I made the decision to stay ‘just three more months’ two years ago, thinking he would change his mind / be ready. It’s now two years on, and nothing has changed. I’m 37 and my chances of having children are now low (I live in a country where IVF is not permitted for single women), and it’s harder to leave than it was due to the time invested, the hopes, lost opportunities.
I know it’s not easy to leave someone you love, when everything - except this - is fine. So please trust me when I say I don’t give this advice lightly. If I could rewind two years and do it again, despite how much I love my partner deeply, I would leave. The resentment is growing, and I wish I hadn’t let it come to this.
It’s horrible, but please put yourself and your future happiness first when making this decision.